Study of Impurity Distribution and Transport Coefficients - - PowerPoint PPT Presentation

SLIDE 1

Study of Impurity Distribution and Transport Coefficients Determination in ITER like Plasma Coefficients Determination in ITER-like Plasma

Liping Zhu, Woochang Lee, Gunsu Yun, Hyeon K. Park

Pohang University of Science and Technology, Pohang 790-784, Korea

85th KPS Meeting 85 KPS Meeting (Changwon, October 21-23, 2009)

SLIDE 2

Contents

• Introduction of MIST code
• Main plasma profiles and parameters used in this study
• Impurity distribution in ITER-like plasma
• Steady state case
• Time dependent case
• Determination of impurity transport coefficients in

ITER-like plasma

SLIDE 3

• I. Introduction of MIST code (1)

An impurity transport simulation code, Multiple Ionization State Transport (MIST), p y p , p p ( ), which is designed for circular cross-section plasma, has been used to study the radial distribution of impurities in various charge states in the standard ITER-like plasma parameters. The code solves for density of ions in each charge state of the impurity and their associated radiation rates using atomic physics appropriate for these low-density and high-temperature plasmas high-temperature plasmas. The expression governing the time evolution of a given impurity charge-state density in space and time has the form: in space and time has the form: where is particle flux density its general form is

1 1 1 1

1 ( ) ( )

q q q q q q q q q q q q

n n r I n I R n R n S t r r τ

− − + +

∂ ∂ = − Γ + − + + − + ∂ ∂

Γ

where is particle flux density, its general form is : particle diffusion coefficient : convective velocity ( ) ( )

q q q q q

n D r r n r υ ∂ Γ = − + ∂

( ) r υ

q

Γ

( ) D r : particle diffusion coefficient,

: convective velocity , , and are functions of charge state, radius, and time.

( )

q r

υ

q

I

q

R

q

τ

q

S

( )

q

D r

SLIDE 4

• I. Introduction of MIST code (2)

Assuming symmetry in all but the radial

a

• ne zone

ssu g sy e y bu e d coordinate (cylindrical geometry), the plasma has been divided into 50 radial zones from the plasma center to the scrape

r

• ff layer.

R

The impurity transport ffi i t b d t i d b coefficients can be determined by comparing the code results with measured local radiation power or spectral line intensities spectral line intensities.

SLIDE 5

• II. Plasma profiles & main parameters used in this study

ITER is a joint international research and development project that aims to emonstrate the scientific and technical feasibility of fusion power.

20 25

T

Major radius, R 620 i di [ ]

cm

[ ]

10 15

Te, Ti (keV)

Te

Ti

Minor radius, a 200 Center 23.3 Edge 0.43 Center 19.3

[ ]

keV

[ ]

cm

e

T

i

T

e

T

[ ]

keV

[ ]

keV

0.0 0.2 0.4 0.6 0.8 1.0 5

Normalized minor radius (r/a)

Center 19.3 Edge 2.4 Center 10.67 Edge 0.55

i

T

e

n

i

T

[ ]

keV

[ ]

keV

19 3

10 m− ⎡ ⎤ ⎣ ⎦

e

n

19 3

10 m− ⎡ ⎤ ⎣ ⎦ Electron & ion temperature

( )

8 10 12 5 6 7 8

• r q

2 4 6

ne(x10

13cm

• 3)

1 2 3 4

Safety facto

Electron density Safety factor q

Reference: ‘Design study for ITER High Resolution x-ray Spectroscopy Array’, Pobin Barnsley, EFDA-JET-CP(04)01/09

0.0 0.2 0.4 0.6 0.8 1.0 2

Normalized minor radius (r/a)

0.0 0.2 0.4 0.6 0.8 1.0 1

Normalized minor radius (r/a)

SLIDE 6

Impurity concentration determination for steady state case

The main limitation to allowed impurity concentration is not the contribution to Zeff, but the impurity radiated power, there being a broad operating range between about 100kW and 10 MW.

Reference:

AREXP

D AC AR

r D(r)=D +D ( ) a

2 AC

D =0.1~3.0m /s

AR AC

D 0,2 D = ×

AREXP

D =1

2

( ) [ 2 D(r) ]

VR

r V r C a = × − × 0 ~10

VR

C =

(‘Power Radiated from ITER and CIT by Impurities’, J. Cummings, PPPL-2702)

10

10

He

9 10

He

a

We use:

2

( ) 0.1 [-2 ( ) ] r V r D r a = × ×

4 2

1 10 / D cm s = ×

10

6

10

7

10

8

10

9

wer(Watts) Be C Cu Ar Kr

3 4 5 6 7 8

f

Be C Cu Ar Kr

10

3

10

4

10

5

10

Radiated pow

2 3

Zeff

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10

2

Impurity concentration (nimp/ne)

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

1

Impurity concentration (nimp/ne)

Total radiated power Z effective

Maximum impurity concentration

/

i

n n

He Be C Cu Ar Kr 25% 4% 1.5%

Maximum impurity concentration

/

imp e

n n

4

1.5 10− ×

4

6 10− ×

5

8 10− ×

SLIDE 7

• III. Impurity distribution in steady state case (1)

10

14

He2+

Impurity concentration

10

11

10

12

10

13

e Density (cm-3)

C6+ Be4+ He2+

He2+ He1+

He Be C Cu 10% 1% 0.5% 2e-5

The 4 impurity species are

10

9

10

10

Charge State

Be4+ Be3+ Be2+ C6+ C5+ C4+ C3+ C2+

The 4 impurity species are calculated respectively.

Radiated power (MW):

0.0 0.2 0.4 0.6 0.8 1.0

10

8

Normalized minor radius (r/a)

9x10

11

C 29

He Be C Cu 4.4 2.27 3.25 1.16

Impurity charge state density (He, Be, C)

p ( )

4x10

11

5x10

11

6x10

11

7x10

11

8x10

11

particles/cm

2/s)

Cu29+ Cu28+ Cu27+ Cu26+ Cu25+ Cu24+ Cu23+ Cu22+ Cu21+

1.0x10

9

1.2x10

9

1.4x10

9

1.6x10

9

nsity (cm

• 3)

Cu27+ Cu28+ Cu29+

Cu29+ Cu28+ Cu27+ Cu26+ Cu25+ Cu24+ Cu23+ Cu22+ Cu21+ Cu20+

• 1x10

11

1x10

11

2x10

11

3x10

11

Cu26+ Cu28+

ansport flux density (p

Cu20+

Cu29+ 2 0 10

8

4.0x10

8

6.0x10

8

8.0x10

8

Charge State De

Cu25+ Cu26+ 0.0 0.2 0.4 0.6 0.8 1.0

• 3x10

11

• 2x10

11

Normalized minor radius (r/a)

Cu27+

Tra

0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10

8

Normalized minor radius (r/a)

Impurity charge state density (Cu) Transport flux density (Cu)

SLIDE 8

• III. Impurity distribution in steady state case (2)

10

• 1

He Be C

1.4 He Be C 10

• 2

n power(W/cm3)

C Cu

He

1.1 1.2 1.3

Zeff

C Cu

Local radiation Be C Cu

0.9 1.0

Z

10

16

He1+

0.0 0.2 0.4 0.6 0.8 1.0 10

• 3

Normalized minor radius (r/a)

0.0 0.2 0.4 0.6 0.8 1.0 0.8

Normalized minor radius (r/a)

10

16

Effective atomic number Local radiation power

10

12

10

13

10

14

10

15

• s/cm3/sec)

He1+ C2+ C3+ C4+ C5+

C5+

10

15

C5+ C3+ C3+ C2+

• tos/s/cm

2/ion)

C2+ He1+

10

7

10

8

10

9

10

10

10

11

C4+ Line emission(photo He1+

10

13

10

14

C5+ C5+ C4+ C3+ C3+ C3+ C3+ C3+

Line brightness (pho

0.0 0.2 0.4 0.6 0.8 1.0 10

6

10

Normalized minor radius (r/a)

50 100 150 200 250 300 350 400 1200 1600 10

C5+

Wavelength (Angstrom)

Line emission (photos/cm3/s) Line emission brightness (photos/s/cm2/ion)

SLIDE 9

• IV. Impurity distribution in time dependent case (1)

Impurity charge state density Injected Krypton atom number: 5.3e17

2.0x10

9

2.4x10

9

m-3)

Kr21+ Kr19+

Kr36+ Kr35+ Kr34+ Kr33+ Kr32+ Kr31+ Kr30+ Kr29+ Kr28+

Kr20+

10

2.5x10

10

3.0x10

10

m-3)

Kr1+

pu y c a ge s a e de s y jec ed yp o a o u be : 5.3e 7

8.0x10

8

1.2x10

9

1.6x10

9

rge state density (cm

Kr28+ Kr27+ Kr26+ Kr25+ Kr24+ Kr23+ Kr22+ Kr21+ Kr20+ Kr19+ Kr18+ Kr17+ Kr16+

1.0x10

10

1.5x10

10

2.0x10

10

rge state density (cm

40 80 120 160 200 0.0 4.0x10

8

Minor radius (cm) Cha

Kr16+ Kr15+ Kr14+ Kr13+ Kr12+ Kr11+ Kr10+ Kr9+

40 80 120 160 200 0.0 5.0x10

9

Char Minor radius (cm)

time = 0.0 s time = 0.001 s

( )

4x10

8

5x10

8

cm-3)

Kr27+ Kr25+

Kr36+ Kr35+ Kr34+ Kr33+ Kr32+ Kr31+ Kr30+ Kr29+ Kr28+ Kr27+

Kr26+ 1.6x10

8

2.0x10

8

(cm-3)

Kr36+ Kr35+ Kr34+ Kr33+ Kr32+ Kr31+ Kr30+ Kr29+ Kr28+

Kr34+

2x10

8

3x10

8

harge state density (c

Kr27 Kr26+ Kr25+ Kr24+ Kr23+ Kr22+ Kr21+ Kr20+ Kr19+ Kr18+ Kr17+ Kr16+ Kr15+

8.0x10

7

1.2x10

8

Charge state density Kr32+ Kr33+

Kr28 Kr27+ Kr26+ Kr25+ Kr24+ Kr23+ Kr22+ Kr21+ Kr20+

40 80 120 160 200 1x10

8

Minor radius (cm) Ch

Kr15+ Kr14+ Kr13+ Kr12+ Kr11+ Kr10+ Kr9+

40 80 120 160 200 0.0 4.0x10

7

Minor radius (cm) C

time = 0.01s time = 0.05s

SLIDE 10

• IV. Impurity distribution in time dependent case (2)

7

5.0x10

7

Kr36+ Kr35+

1.2x10

8

Kr36+ K 35+

2 5 10

7

3.0x10

7

3.5x10

7

4.0x10

7

4.5x10

7

Kr34+ Kr35+

nsity (cm-3)

Kr35+ Kr34+ Kr33+ Kr32+ Kr31+ Kr30+ Kr29+

6 0 10

7

8.0x10

7

1.0x10

8

Kr35+ Kr34+ Kr33+ Kr32+ Kr31+ Kr30+ Kr29+

Kr34+

nsity (cm-3)

5 0 10

6

1.0x10

7

1.5x10

7

2.0x10

7

2.5x10

7

Kr32+ Kr33+

Charge state de

Kr36+ 2.0x10

7

4.0x10

7

6.0x10

7

Kr32+ Kr33+ Kr35+

Charge state de

40 80 120 160 200 0.0 5.0x10

6

Kr32+

Minor radius (cm)

7

Kr36+ K 36+

time = 0.15s time = 0.5s

40 80 120 160 200 0.0

Minor radius (cm)

1.0x10

7

1.2x10

7

1.4x10

7

Kr34+ Kr35+

sity (cm-3)

Kr36+ Kr35+ Kr34+ Kr33+ Kr32+ Kr31+ Kr30+ Kr29+

1.5x10

6

2.0x10

6

Kr36+ Kr35+ Kr34+ Kr33+ Kr32+ Kr31+ Kr30+ Kr29+

Kr34+ Kr35+

sity (cm-3)

4.0x10

6

6.0x10

6

8.0x10

6

Kr33+ Kr35

Charge state dens

Kr36+ 5.0x10

5

1.0x10

6

Kr33+

Charge state dens

Kr36+ 40 80 120 160 200 0.0 2.0x10

6

Minor radius (cm)

Kr32+ Kr33+ 40 80 120 160 200 0.0

Minor radius (cm)

Kr32+ Kr33+

time = 1.5s time = 3.0s

SLIDE 11

• IV. Impurity distribution in time dependent case (3)

10

14

m

2) Kr5+(57nm) Kr5+(46.6nm) Kr6+(58.5nm) K 24 (15 91 )

Kr24+(15 91nm)

10

9

10

10

Kr34+(0.0965nm) Kr35+(0.0928nm) 10

8

10

10

10

12

ness(photos/sec/ion/cm

Kr24+(15.91nm) Kr25+(17.86nm) Kr34+(0.0965nm) Kr35+(0.0928nm)

Kr24+(15.91nm) Kr34+(0.0965nm) Kr35+(0.0928nm) Kr25+(17.86nm)

10

6

10

7

10

8

10

9

ion(photos/cm

3/s)

( ) Kr24+(15.91nm) Kr25+(17.86nm) Kr5+(57nm) Kr5+(46.6nm) Kr6+(58.5nm) 1E-3 0.01 0.1 1 10

2

10

4

10

6

Line emission bright

1E 3 0 01 0 1 1 10

2

10

3

10

4

10

5

Line emiss

10

6

tts)

1E 3 0.01 0.1 1

Time (s)

1E-3 0.01 0.1 1

Time (s) 10

10

Kr34+(0 0965nm)

14

10

15

Kr24+(15 91nm)

1E-3 0.01 0.1 1 10

2

10

3

10

4

10

5

Total radiated power (Wat Time (s)

Line emission brightness Line emission at r =2.1 cm

6

10

7

10

8

10

9

Kr34+(0.0965nm) Kr35+(0.0928nm) Kr24+(15.91nm) Kr25+(17.86nm) Kr5+(57nm) Kr5+(46.6nm) Kr6+(58.5nm)

hotos/cm

3/s)

10

9

10

10

10

11

10

12

10

13

10

14

photos/cm

3/s)

Kr24+(15.91nm) Kr25+(17.86nm) Kr5+(57nm)

( )

Total radiated power

10

3

10

4

10

5

10

6

Line emission(p

10

3

10

4

10

5

10

6

10

7

10

8

Line emission(p

1E-3 0.01 0.1 1 10

2

Time (s)

1E-3 0.01 0.1 1 10

2

Time (s)

Line emission at r =199.5 cm Line emission at r =102.9 cm

SLIDE 12

• V. Determination of transport coefficients in ITER-like plasma

Compare the local radiation power profiles of code calculated results and the f dj t th t t ffi i t til t h i hi d

10

15

3

10

13

10

• 2

reference; adjust the transport coefficients until a match is achieved. The reference was calculated by using the SANCO impurity transport code.

Argon concentration:

5

1 10− ×

10

12

10

13

10

14

photos/cm3/s) hotos/cm3) Calculated line emission(photos/cm3/s)

10

10

10

11

10

12

Ar17+ Ar16+

10

wer (W/cm3) Reference value Calculated result

8

10

9

10

10

10

11

Ar17+ Ar16+ Reference emissivity (photos/cm3) Line emission(p Emissivity (ph

10

8

10

9

10

10

• 3

Local radiation pow

80 120 160

0 .3

r v ( r ) = 2 2 0 -3 5 0 ( ) a

y (cm/s)

0.0 0.2 0.4 0.6 0.8 1.0

10

8

Normalized minor eadius (r/a)

10

7

0.0 0.2 0.4 0.6 0.8 1.0 10

• 4

Normalized minor radius (r/a)

Determined transport coefficients:

• 80
• 40

40

ated convective velocity

More accurate method: compare the

p

4 2

8 10 / D cm s = ×

0.3

r v(r)=220-350( ) a

0.0 0.2 0.4 0.6 0.8 1.0

• 160
• 120

Calcula Normalized minor radius (r/a)

More accurate method: compare the line emission spectrum of code calculation results and the reference.

Reference: ‘Design study for ITER High Resolution x-ray Spectroscopy Array’, Pobin Barnsley, EFDA-JET-CP(04)01/09

SLIDE 13

Summary & Future work

Summary Summary

Study of impurity distribution has been done in both steady state and time dependent cases Here the impurity profiles include charge state time dependent cases. Here, the impurity profiles include charge state density, effective atomic number, local & total radiation power, line emission & brightness for variety possible impurity species, etc. In steady state case, the impurity transport coefficients have been determined by comparing the local radiation power profile between the MIST code result and the reference.

Future work

Modify the source code to calculate Z >56 case.